Beyond the relativistic mean-field approximation (III): collective Hamiltonian in five dimensions

Abstract

The framework of relativistic energy density functionals is extended to include correlations related to restoration of broken symmetries and fluctuations of collective variables. A new implementation is developed for the solution of the eigenvalue problem of a five-dimensional collective Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The model is tested in a series of illustrative calculations of potential energy surfaces and the resulting collective excitation spectra and transition probabilities of the chain of even-even gadolinium isotopes.

arXiv comment53 pages, 23 figures, accepted for publication in Phys. Rev. C

References in corpus (13)

• Relativistic Continuum Hartree Bogoliubov Theory for Ground State Properties of Exotic Nuclei
• Nuclear Ground State Observables and QCD Scaling in a Refined Relativistic Point Coupling Model
• Particle number projection with effective forces
• Configuration mixing of angular-momentum and particle-number projected triaxial HFB states using the Skyrme energy density functional
• Particle-Number Projection and the Density Functional Theory
• Microscopic description of nuclear quantum phase transitions
• Beyond the relativistic mean-field approximation (II): configuration mixing of mean-field wave functions projected on angular momentum and particle number
• Beyond the relativistic mean-field approximation: configuration mixing of angular momentum projected wave functions
• Effects of beta-gamma coupling in transitional nuclei and the validity of the approximate separation of variables
• Solution of the Skyrme-Hartree-Fock equations in the Cartesian deformed harmonic oscillator basis. (I) The method
• Collective quadrupole excitations in the 50<Z,N<82 nuclei with the generalized Bohr Hamiltonian
• Time-odd triaxial relativistic mean field approach for nuclear magnetic moments
• A beyond mean field analysis of the shape transition in the Neodymium isotopes

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